Mixing effect and skin effect on radical solute transport around an injection well
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摘要:
注水井理论模型研究一直是水文地质学领域的热点问题。充分考虑含水层的非均质性，利用两区MIM(Mobile-Immobile)对流扩散模型来描述溶质在含水层中的运移过程，同时考虑表皮效应和井筒混合效应，建立一种描述注入井附近含水层溶质径向运移的动力学模型。并采用Laplace变换、Stehfest数值逆变换得到了该动力学模型的半解析解。然后改变表皮区的有效孔隙度和径向弥散度以及井筒的半径，来分析固定观测点的溶质穿透曲线和溶质浓度分布曲线的变化规律。研究表明，井筒混合效应和表皮效应对穿透曲线、溶质径向运移过程和影响区域均有着非常显著的影响。在考虑井筒混合效应时，井筒半径越大，井筒效应越明显。而表皮区域有效孔隙度越大，溶质的迁移扩展速率越小；径向弥散度越大，观测点的溶质浓度曲线越陡峭，表明该点的溶质浓度变化速率较快，且能更早达到稳定值。与前人研究相比，本研究模型能更好地描述注水井中的溶质径向弥散过程。
Abstract:Objective The conceptual model of the single-well push test is a hot topic in groundwater hydrogeology.
Methods In this study, a new mathematical model was developed for radial solute transport in an aquifer near injection wells. The heterogeneity of the aquifer was considered, and the MIM (Mobile-Immobile) convective diffusion model was used to describe the solute transport process in the aquifer. The skin effect and mixing effect are also included in this conceptual model. The semi-analytical solution was derived by using the Laplace transform and Stehfest numerical inverse transform methods. The influence of effective porosity and radial dispersion of the skin zone and the radius of the wellbore on the solute breakthrough curves (BTCs) of a fixed observation point and solute concentration distribution curves at given times were investigated.
Results Results show that wellbore mixing and skin effects have significant impacts on BTCs, solute radial transport processes and the influence area. The larger the radius of the wellbore is, the more obvious the wellbore mixing effect is. For the skin zone, a larger porosity leads to a smaller velocity of solute migration. The larger the radial dispersion is, the steeper the solute concentration curve of the observation point is, indicating that the solute concentration changes at a faster rate and can reach a stable value earlier.
Conclusion Compared with previous studies, this model can better describe the solute radial dispersion process near the injection wells.
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Key words:
- skin effect /
- mixing effect /
- injection well /
- radial solute transport
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图 1 注水井溶质径向迁移概念模型
B为承压层厚度；Q为注入量；γw为注入井半径；r1为表皮区+注入井半径；r为离井筒中心的径向距离
Figure 1. Conceptual model of radial solute transport in a single push well
图 2 不同观测点A、B的穿透曲线半解析解和数值解对比结果
Figure 2. Comparison of the semianalytical solution and numerical solution of BTCs at observation points A and B
图 3 不同表皮区有效孔隙度(θ1m)时观测点A的穿透曲线(a)及溶质浓度径向分布曲线(b)
Figure 3. Breakthrough curves of observation point A (a) and concentration distribution curves (b) for different effective porosities (θ1m) in the skin zone
图 4 不同表皮区径向弥散度(α1)时观测点A的穿透曲线(a)及溶质浓度径向分布曲线(b)
Figure 4. Breakthrough curves of observation point A (a), and concentration distribution curves (b) for different radical dispersivities (α1) in the skin zone
图 5 不同注入井半径(rw)时观测点A的穿透曲线
Figure 5. Breakthrough curves of observation point A for different wellbore radii (rw)
图 6 当t=5 h时(a)和t=30 h时(b)不同注入井半径(rw)的溶质浓度径向分布曲线
Figure 6. Concentration distribution curves for different well radii (rw) of wellbore when t=5 h (a) and t=30 h (b)
表 1 无量纲参数定义
Table 1. Definitions of dimensionless variables
$ r_{\mathrm{D}}=\frac{r}{\alpha_2}$ $ t_{\mathrm{D}}=\frac{Q t}{2 \pi B \alpha_2^2 \theta_{2 \mathrm{~m}} R_{2 \mathrm{~m}}}$ $ C_{1 \mathrm{mD}}=\frac{C_{1 \mathrm{~m}}}{C_0}$ $ C_{1 \mathrm{imD}}=\frac{C_{1 \mathrm{im}}}{C_0}$ $ C_{2 \mathrm{mD}}=\frac{C_{2 \mathrm{mD}}}{C_0}$ $ C_{2 \mathrm{imD}}=\frac{C_{2 \mathrm{im}}}{C_0}$ $ \lambda_{1 \mathrm{mD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{1 \mathrm{~m}}$ $ \lambda_{2 \mathrm{mD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{2 \mathrm{~m}}$ $ \beta_2=\frac{\theta_{2 \mathrm{im}}}{\theta_{2 \mathrm{~m}}}$ $ \beta_1=\frac{\theta_{1 \mathrm{im}}}{\theta_{1 \mathrm{~m}}}$ $ \varepsilon_1=\frac{R_{1 \mathrm{~m}}}{R_{2 \mathrm{~m}}}$ $ \varepsilon_2=\frac{R_{1 \mathrm{im}}}{R_{2 \mathrm{~m}}}$ $ \varepsilon_3=\frac{R_{2 \mathrm{im}}}{R_{2 \mathrm{~m}}}$ $ \beta=\frac{V_{\mathrm{w}}}{2 \pi B \theta_{2 \mathrm{~m}} R_{2 \mathrm{~m}} \alpha_2^2}$ $ k_1=\frac{\alpha_1}{\alpha_2}$ $ k_2=\frac{\theta_{2 \mathrm{~m}}}{\theta_{1 \mathrm{~m}}}$ $ \omega_{1 \mathrm{D}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q \theta_{1 \mathrm{im}}} \omega_1$ $ \omega_{2 \mathrm{D}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q \theta_{2 \mathrm{im}}} \omega_2$ $ \lambda_{1 \mathrm{imD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{1 \mathrm{im}}$ $ \lambda_{2 \mathrm{imD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{2 \mathrm{im}}$ 
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表 2 模型参数默认取值
Table 2. Default parameter values used in this study
参数 值 参数 值 Q/(m3·h-1) 2.5 B/m 5 rw/m 0.1 r1/m 0.8 θ1m 0.15 θ2m 0.15 θ1im 0.1 θ2im 0.1 ω1/(1·h-1) 0.05 ω2/(1·h-1) 0.05 α1/m 0.5 α2/m 0.5
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